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Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux. (English) Zbl 0619.76091
The artificial viscosity (Q) method of von Neumann and Richtmyer is a tremendously useful numerical technique for following shocks wherever and whenever they appear in the flow. We show that it must be used with some caution, however, as serious Q-induced errors (on the order of 100 %) can occur in some strong shock calculations. We investigate three types of Q errors: 1. Excess Q heating, of which there are two types: (a) excess wall heating on shock formation and (b) shockless Q heating; 2. Q errors when shocks are propagated over a nonuniform mesh; and 3. Q errors in propagating shocks in spherical geometry.

76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
65Z05 Applications to the sciences
Full Text: DOI
[1] Von Neumann, J.; Richtmyer, R.D., J. appl. phys., 21, 232, (1950)
[2] Noh, W.F., Ucrl-89623, (1983), Lawrence Livermore National Laboratory Livermore, CA, (unpublished)
[3] Richtmyer, R.D.; Morton, K.W., Interscience tracts in pure and applied mathematics, ()
[4] Trulio, J.F.; Trigger, K.R., Ucrl-6267, (1961), Lawrence Livermore National Laboratory Livermore, CA, (unpublished)
[5] Noh, W.F., Ucrl-7463, (1963), Lawrence Livermore National Laboratory Livermore, CA, (unpublished)
[6] White, J., J. comput. phys., 12, 553, (1973)
[7] Colella, P.; Woodward, P., Lbl-14661, (1982), Lawrence Berkeley Laboratory Berkeley, CA, (unpublished)
[8] Schulz, W.D., J. math. phys., 5, 133, (1964)
[9] {\scP. P. Whalen}, Los Alamos National Laboratory Memo X-DO-PPW (3/84)-02, Los Alamos, NM, 1984 (unpublished).
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